\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space

This paper is dedicated to the memory of the late Bob Glassey

CK is supported in part by National Science Foundation under Grant No. 1900923 and the Brain Pool program (NRF-2021H1D3A2A01039047) of the Ministry of Science and ICT in Korea

Abstract Full Text(HTML) Related Papers Cited by
  • Following closely the classical works [5]-[7] by Glassey, Strauss, and Schaeffer, we present a version of the Glassey-Strauss representation for the Vlasov-Maxwell systems in a 3D half space when the boundary is the perfect conductor.

    Mathematics Subject Classification: Primary: 35Q61, 35Q83; Secondary: 35Q70.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] Y. Cao and C. Kim, On some recent progress in the Vlasov-Poisson-Boltzmann system with diffuse reflection boundary, Recent Advances in Kinetic Equations and Applications, Springer INdAM Series, 48 (2021).
    [2] Y. CaoC. Kim and D. Lee, Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains, Arch. Rational Mech. Anal., 233 (2019), 1027-1130.  doi: 10.1007/s00205-019-01374-9.
    [3] J. Cooper and W. Strauss, The initial boundary problem for the Maxwell equations in the presence of a moving body, SIAM J. Math. Anal., 16 (1985), 1165-1179.  doi: 10.1137/0516086.
    [4] G. Federici, et al, Plasma-material interactions in current tokamaks and their implications for next step fusion reactors, Nucl. Fusion, 41 (2001).
    [5] R. T. Glassey, The Cauchy Problem in Kinetic Theory, Society for Industrial and Applied Mathematics, 1996. doi: 10.1137/1.9781611971477.
    [6] R. T. Glassey and J. Schaeffer, The relativistic Vlasov-Maxwell system in two space dimensions. Ⅰ, Arch. Rational Mech. Anal., 141 (1998), 331-354.  doi: 10.1007/s002050050079.
    [7] R. T. Glassey and J. Schaeffer, The relativistic Vlasov-Maxwell system in two space dimensions. Ⅱ, Arch. Rational Mech. Anal., 141 (1998), 355-374.  doi: 10.1007/s002050050080.
    [8] R. T. Glassey and W. A. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Arch. Rational Mech. Anal., 92 (1986), 59-90.  doi: 10.1007/BF00250732.
    [9] R. T. Glassey and W. A. Strauss, High velocity particles in a collisionless plasma, Math. Methods Appl. Sci., 9 (1987), 46-52.  doi: 10.1002/mma.1670090105.
    [10] D. GriffithIntroduction to Electrodynamics, Cambridge University Press, 4th edition, 2017. 
    [11] Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Comm. Math. Phys., 154 (1993), 245-263.  doi: 10.1007/BF02096997.
    [12] Y. Guo, Regularity for the Vlasov equations in a half space, Indiana Univ. Math. J., 43 (1994), 255-320.  doi: 10.1512/iumj.1994.43.43013.
    [13] J. D. Jackson, Classical Electrodynamics, Wiley, 3rd edition, 1998. doi: 10.1119/1.19136.
    [14] X. Liu, F. Yang, M. Li and S. Xu, Generalized boundary conditions in surface electromagnetics: Fundamental theorems and surface characterizations, Appl. Sci., 9 (2019). doi: 10.3390/app9091891.
    [15] J. Luk and R. M. Strain, A new continuation criterion for the relativistic Vlasov-Maxwell system, Comm. Math. Phys., 331 (2014), 1005-1027.  doi: 10.1007/s00220-014-2108-8.
    [16] K. McDonald, Electromagnetic fields inside a perfect conductor, Unpublished note.
    [17] T. T. NguyenT. V. Nguyen and W. A. Strauss, Global magnetic confinement for the 1.5D Vlasov-Maxwell system, Kinetic and Related Models, 8 (2015), 153-168.  doi: 10.3934/krm.2015.8.153.
  • 加载中
SHARE

Article Metrics

HTML views(281) PDF downloads(296) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return